What's the difference between a "racist" and a "racially sensitive" remark?

When I hear "Racist remark", I imagine a remark that places a person's ethnicity as the cause of their failing, or in some way contributing to their inadequacy, or part of a verbal attack because of their race.

"Racially sensitive remark" makes me think it was a word that, in itself, is not a direct insult towards a person. For example, the word "nigger" is considered racially sensitive because of the history around the word, not necessarily because it confers any meaning (aside from that the person is black).

The word "sensitive" in the phrase "racially sensitive" means "touchy."

sensitive = calling for tact, care, or caution in treatment

The difference between "a racist remark" and "racially sensitive words" is that "racist" can mean a conscious, deliberate, and unrepentant act of insulting.

The expression "racially sensitive," on the other hand, is open to the interpretation and possibility that “what was said was not intended as an insult.”

In this case, a racist remark is one where insult is meant by saying the words. A racially sensitive remark is one that uses words that could be insulting or abusive, but depending on the context.

Note the square brackets indicating omission and/or insertion. The BBC are tip-toeing around the words Judge Howard Riddle used in his summation by removing them and replacing them with a watered-down summary.

The judge actually wrote in his judgment (PDF linked from the article):

There is also no dispute that John Terry directed the words “black cunt” in the direction of Anton Ferdinand.

It's not the BBC's place to use the word racist as they would then be making a judgment of guilt about John Terry. In fact, the judge also said:

... the issue for this court to decide is not whether Mr Terry is a racist, in the broadest sense of the word... The issue between the defendant and the Crown is whether Mr Terry uttered the words “fucking black cunt” by way of insult. If he did then the offence is made out, regardless of what may have motivated him.

Additionally, the court reached a not guilt verdict. The judge wrote of Terry:

It is therefore possible that what he said was not intended as an insult, but rather as a challenge to what he believed had been said to him.

In those circumstances, there being a doubt, the only verdict the court can record is one of not guilty.

Instead, like most news sources, the BBC don't want to publish the words directly in their article (but have no problem publishing the judgment document which repeats them many times), and have referred to them obliquely.

I can explain the distinction best with an example:

Some years ago there was a local news story of a mall Santa who was fired for calling a little black boy a monkey. He was accused of racism. The issue with this is... people call small children monkeys all the time. They’re loud and climb on things and generally mischievous and chaotic... i.e. monkeys. I don’t doubt this man called lots of kids monkeys. He was (I believe) simply trying to be silly and joke with the kid a bit. (And yes, I call my own daughter “monkey” fairly often. We’re white.)

But there is a definite history of black people in America being called monkeys, apes and so forth as a racist insult. The mall Santa probably should have been aware of this and avoided this particular joke. So his comment was not racist, in that he did not think of it, nor intend it, as a racial slur; but it was racially sensitive because of the ugly history of the word and similar being used as a slur.

Racially sensitive = you may not be racist, but you still should have realized that would be seen as offensive